Answered: Viscous fluid occupies the region 0

Engineering

Mechanical Engineering

Viscous fluid occupies the region 0

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Properties of Fluids

The term fluid represents a type of substance that can easily change its shape under any external pressure/force and can flow. Fluids can acquire any shape in which it is stored and can resist normal stresses but cannot resist shear stress in rest condition. Whenever external shear stress is applied to fluids, it starts to flow. The fluids may be liquid or gas. Example- water, air, etc.

Question

Viscous fluid occupies the region 0 < z<h between two rigid boundaries z = 0 and z = h.
The lower boundary is at rest, the upper boundary rotates with constant angular velocity
N about the z-axis. Show that a steady solution of the full Navier-Stokes equations with
flow only in the 0-direction of the form
u = u9(r, z)eo
is not possible (i.e., show any rotary motion ue(r,z) in this system must be accompanied
by a secondary flow where u; or uz # 0).

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